Attractors for stochastic reaction-diffusion equation with additive homogeneous noise

Abstract

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$\mathbb{H}^1$-Random attractors for 2D stochastic convective Brinkman-Forchheimer equations in unbounded domains

“…The concept of an asymptotically compact cocycle was introduced in [14] and the authors proved the existence of attractors fornon-autonomous 2D NSE. Later, several authors used this method to prove the existence of random attractors in unbounded domains, see for example [9,12,13,27,35,36,38,47,49,53,54,58] etc. The existence of a unique random attractor for the 2D and 3D SCBF equations (1.2) perturbed by additive rough noise in H is proved in [38].…”

Random attractors for 2D and 3D stochastic convective Brinkman-Forchheimer equations in some unbounded domains

“…The concept of an asymptotically compact cocycle was introduced in [16] and authors have established the existence of attractors for the non-autonomous 2D Navier-Stokes equations. Later, this concept has been utilized to prove the existence of random attractors for several SPDEs like 1D stochastic lattice differential equation [5], stochastic Navier-Stokes equations on the 2D unit sphere [4], stochastic g-Navier-Stokes equations [27,36,39], stochastic nonautonomous Kuramoto-Sivashinsky equations [38], stochastic heat equations in materials with memory on thin domains [48], stochastic reaction-diffusion equations [6,47,51], 3D stochastic Benjamin-Bona-Mahony equations [51], etc and the references therein.…”